Question

1. the expression \\(\frac{1}{2}a(b + c)\\) can be used to find the area of the trapezoid. what is the area of the trapezoid when \\(a = 6\\), \\(b = 5\\), and \\(c = 7\\)? (example 4)

Explanation:

Step1: Substitute the values

We are given the formula for the area of a trapezoid \( \frac{1}{2}a(b + c) \), and we need to substitute \( a = 6 \), \( b = 5 \), and \( c = 7 \) into this formula. So we get \( \frac{1}{2} \times 6\times(5 + 7) \).

Step2: Simplify the expression inside the parentheses

First, we simplify the expression inside the parentheses: \( 5 + 7 = 12 \). Now the formula becomes \( \frac{1}{2} \times 6\times12 \).

Step3: Multiply the numbers

Next, we multiply \( \frac{1}{2} \) and \( 6 \) first. \( \frac{1}{2} \times 6 = 3 \). Then we multiply this result by \( 12 \): \( 3\times12 = 36 \).

Answer:

The area of the trapezoid is \( 36 \) square meters.